In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimat...In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the L^P（R^n） （1 〈 p 〈 ∞） boundedness and a weak type LlogL estimate for the corresponding maximal operator.展开更多
LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives...LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈Lipαt(Sn-1) (0 <α≤1) and implies the LP(Rn) (1 < p <∞) boundedness for the operator TA.Some endpoint estimates are also established.展开更多
A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogen...A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.展开更多
In this paper, we prove that the maximal operatorsatisfiesis homogeneous of degree 0, has vanishing moment up to order M and satisfies Lq-Dini condition for some
Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz...Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.展开更多
The behavior on the space L^∞（R^n） for the multilinear singular integral operator defined by TAf（x）=∫RnΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）△A（y）（x-y））f（y）dy is considered, where 12 is homogeneous of deg...The behavior on the space L^∞（R^n） for the multilinear singular integral operator defined by TAf（x）=∫RnΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）△A（y）（x-y））f（y）dy is considered, where 12 is homogeneous of degree zero, integrable on the unit sphere and has vanishing is considered, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishingmoment of order one, A has derivatives of order one in BMO（R^n）. It is proved that if Ω satisfies some minimum size condition and an L1-Dini type regularity condition, then for f ∈ L^∞（R^n）, TAf is either infinite almost everywhere or finite almost everywhere, and in the latter case, TAf ∈ BMO（R^n）.展开更多
文摘In this paper, some mapping properties are considered for the maximal multilinear singular integral operator whose kernel satisfies certain minimum regularity condition. It is proved that certain uniform local estimate for doubly truncated operators implies the L^P（R^n） （1 〈 p 〈 ∞） boundedness and a weak type LlogL estimate for the corresponding maximal operator.
文摘LP(Rn) boundedness is considered for the multilinear singular integral operator defined by where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈Lipαt(Sn-1) (0 <α≤1) and implies the LP(Rn) (1 < p <∞) boundedness for the operator TA.Some endpoint estimates are also established.
文摘A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.
文摘In this paper, we prove that the maximal operatorsatisfiesis homogeneous of degree 0, has vanishing moment up to order M and satisfies Lq-Dini condition for some
基金Supported by the National Natural Science Foundation of China(10971228)Supported by the Science and Technology Innovation Plan for Graduate Students of Jiangsu Educational Department(CXZZll-0633)+1 种基金Supported by the Science and Technology Innovation Plan for Graduate Students of Nangtong University (YKC111051)Supported by the NSF of Nantong University(llZY002)
文摘Let μ be a non-negative Radon measure on R^d which satisfies some growth conditions. The boundedness of multilinear Calderon-Zygmund singular integral operator T and its commutators with RBMO functions on Morrey-Herz spaces are obtained if T is bounded from L^1（μ）χ…χ L^1（μ） to L1/m,∞（μ）.
文摘The behavior on the space L^∞（R^n） for the multilinear singular integral operator defined by TAf（x）=∫RnΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）△A（y）（x-y））f（y）dy is considered, where 12 is homogeneous of degree zero, integrable on the unit sphere and has vanishing is considered, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishingmoment of order one, A has derivatives of order one in BMO（R^n）. It is proved that if Ω satisfies some minimum size condition and an L1-Dini type regularity condition, then for f ∈ L^∞（R^n）, TAf is either infinite almost everywhere or finite almost everywhere, and in the latter case, TAf ∈ BMO（R^n）.
